A Gibbs Sampling Algorithm with Monotonicity Constraints for Diagnostic Classification Models
A Gibbs Sampling Algorithm with Monotonicity Constraints for Diagnostic Classification Models
复制标题
具有单调性约束的诊断分类模型吉布斯采样算法
DOI：
10.1007/s00357-021-09392-7
复制
发表时间：
2021
影响因子：
2
通讯作者：
Templin Jonathan
中科院分区：
文献类型：
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作者：
Yamaguchi Kazuhiro;Templin Jonathan
诊断分类模型(DCM)是具有一组跨类等式约束和附加单调性约束的受限潜在类模型，这两个约束都是为了确保类和模型参数的意义。本文提出了一种基于Gibbs抽样的贝叶斯-马尔可夫链蒙特卡罗估计方法，用于一般单调性约束下的DCMS。对算法的参数恢复进行了仿真研究，结果表明该算法对模型参数的估计是准确的。此外，将该算法与以前提出的Gibbs抽样算法进行了比较，后者仅对对数线性认知诊断模型的主要影响项参数施加约束。新算法具有较小的偏差和较快的收敛速度。还使用该算法对2000年国际学生评估方案的阅读评估数据进行了分析。
Diagnostic classification models (DCMs) are restricted latent class models with a set of cross-class equality constraints and additional monotonicity constraints on their item parameters, both of which are needed to ensure the meaning of classes and model parameters. In this paper, we develop an efficient, Gibbs sampling-based Bayesian Markov chain Monte Carlo estimation method for general DCMs with monotonicity constraints. A simulation study was conducted to evaluate parameter recovery of the algorithm which showed accurate estimation of model parameters. Moreover, the proposed algorithm was compared to a previously developed Gibbs sampling algorithm which imposed constraints on only the main effect item parameters of the log-linear cognitive diagnosis model. The newly proposed algorithm showed less bias and faster convergence. An analysis of the 2000 Programme for International Student Assessment reading assessment data using this algorithm was also conducted.